Volume scattering of radar signals is not a single diagnostic indicator of water ice within permanently shadowed regions near the lunar poles

Technical Summary: Re-evaluating Radar Signatures for Lunar Polar Ice

Problem Statement
Recent research by Sinha et al. interpreted polarimetric radar signatures from doubly shadowed craters near the lunar South Pole as evidence of subsurface water ice. They proposed a combined empirical threshold for the radar Circular Polarization Ratio (CPR) and the Degree of Polarization (DOP) as a refined diagnostic criterion, specifically suggesting that regions with elevated CPR (>1) and low DOP (<0.13) indicate volume scattering caused by thick, sheet-like water ice. This study challenges that interpretation, arguing that the observed variations in CPR and DOP are fully consistent with near-surface roughness rather than subsurface ice, and that the proposed thresholds are not definitive indicators of ice.

Methodology
The authors re-analyzed data from the Chandrayaan-2 Dual-Frequency Synthetic Aperture Radar (DFSAR) using a corrected theoretical framework and comparative statistical analysis:

1. Correction of CPR Calculation: The authors identified an erroneous formula used in the previous study (Sinha et al.) for calculating CPR from DFSAR data. The prior formula applied only to a special case of dihedral scatterers without cross-polarization components. The authors recalculated CPR using the correct definition ($CPR = \sigma^\circ_{SC} / \sigma^\circ_{OC}$), where $\sigma^\circ_{SC}$ and $\sigma^\circ_{OC}$ are the backscattered power coefficients for same-sense and opposite-sense circular polarization, respectively.
2. Data Sampling: Using the corrected formula, the authors sampled the interiors of 10 south polar craters (including Faustini, designated F2) and generated statistical distributions (box and whisker plots) and scatter plots.
3. Comparative Analysis: To distinguish between ice signatures and roughness effects, the authors compared the polarimetric properties of the lunar crater F2 (Faustini) against two non-polar craters with known surface characteristics:
   • Tycho: A fresh, Copernican-age crater (85 km diameter) with abundant centimeter-to-meter scale rocks and impact melt.
   • Byrgius C: A non-polar anomalous crater (13 km diameter) with a surface containing abundant wavelength-scale rocks.
4. Statistical Metrics: The study employed:
   • Kernel Density Estimate (KDE) contour plots for CPR vs. DOP distributions.
   • Ordinary Least Squares (OLS) and Standardized Major Axis (SMA) regression for $\sigma^\circ_{SC}$ vs. $\sigma^\circ_{OC}$ relationships.
   • Spearman correlation coefficients ($\rho_s$) to assess monotonic relationships.
   • Bhattacharya Coefficients (BC) to quantify the overlap between joint distributions.

Key Results

• Impact of Formula Correction: The recalculated CPR values for the 10 south polar craters showed large distributional differences compared to the values reported by Sinha et al. The authors conclude that the CPR ranges presented in the previous work do not represent true CPR values, rendering the claim of ice detection based on elevated CPR (>1) dubious.
• Inconsistency of Proposed Thresholds: Theoretical modeling suggests that thick, clean water ice (exhibiting Coherent Backscatter Effect or CBE) should produce enhanced CPR (>1) combined with DOP values approaching unity (highly polarized). The combination of low DOP (<0.13) and high CPR (>1) proposed by Sinha et al. is invalid for detecting such ice signatures.
• Similarity in Polarimetric Space:
  • CPR-DOP Space: The KDE analysis revealed that the Faustini crater (F2), Tycho, and Byrgius C share substantial overlap (~90%) in their CPR-DOP distributions, particularly in the CPR range of 0.5–1.2 and DOP range of 0.1–0.4. The correlation between CPR and DOP was found to be weak and negligible ($\rho_s$ values were low), indicating they vary largely independently.
  • $\sigma^\circ_{SC}$-$\sigma^\circ_{OC}$ Space: Regression analysis showed that while Byrgius C and Faustini are nearly co-located, Tycho is substantially separated due to higher absolute backscatter magnitudes. This divergence is attributed to Tycho's rough, rock-rich surface causing strong depolarization and complex multiple-bounce scattering.
• Roughness Interpretation: The transitional position of Faustini in both CPR-DOP and $\sigma^\circ_{SC}$-$\sigma^\circ_{OC}$ spaces suggests its surface roughness is intermediate between the other two regions. The authors conclude that the enhanced CPR observed in the doubly shadowed craters is better explained by roughness-induced changes in radar backscatter than by subsurface ice.

Significance and Claims
The paper asserts that volume scattering of radar signals is not a single diagnostic indicator of water ice within permanently shadowed regions. The authors argue that the variations in CPR and DOP observed in lunar polar craters are consistent with varying levels of near-surface roughness.

Consequently, the study claims that robust evidence for thick, sheet-like water ice requires a more stringent set of criteria than previously proposed. Specifically, such evidence necessitates:

1. A combination of strong linear and circular polarization ratios.
2. Enhanced DOP values (approaching unity, indicative of coherent backscatter).
3. A high degree of correlation between radar-bright features and regions of permanent shadow.

The authors maintain that without these combined factors, particularly the high DOP associated with coherent backscatter, the detection of subsurface ice based solely on elevated CPR and low DOP remains unproven.